Indiana University
"Econometric Analysis of Functional Dynamics in the Presence of Persistence."
We introduce an autoregressive model for functional time series with unit roots. The autoregressive operator can be consistently estimated, but its convergence rate and limit distribution are di erent in di erent subspaces. In the unit root subspace, the convergence rate is fast and given by T, while the limit distribution is nonstandard and represented as functions of Brownian motions. Outside the unit root subspace, however, the p limit distribution is Gaussian, although the convergence rate varies and is given by T or a slower rate. The predictor based on the estimated autoregressive operator has a normal limit distribution with a reduced rate of convergence. We also provide the Beveridge-Nelson decomposition, which identi es the permanent and transitory components of functional time series with unit roots, representing persistent stochastic trends and stationary cyclical movements, respectively. Using our methodology and theory, we analyze the time series of yield curves and study the dynamics of the term structure of interest rates.